Electroweak diboson production in association with a high-mass dijet system in semileptonic final states from $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this paper reports the first observation of electroweak diboson production in association with a high-mass dijet system in semileptonic final states with a significance of 7.4$\sigma$, while also measuring cross sections and setting the first exclusion limits on anomalous quartic gauge couplings in this channel within the framework of an effective field theory.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Scientists at the ATLAS detector are like cosmic detectives, smashing protons together to see what tiny pieces fly out. Usually, they look for the "clean" crashes where everything is visible. But sometimes, the crash is messy, with some pieces flying off into the darkness (invisible particles) and others clumping together in a chaotic pile.

This paper is about the ATLAS team successfully spotting a very specific, rare, and messy type of crash: Electroweak Diboson Production with a High-Mass Dijet System.

That's a mouthful, so let's break it down with some everyday analogies.

1. The "Double Trouble" Crash

In the Standard Model of physics, there are force-carrying particles called bosons (like the W and Z bosons). Usually, when protons smash, these bosons are produced alone or in pairs.

• The Goal: The scientists wanted to find a specific event where two of these bosons are created at the same time, plus two other jets of particles (called a "dijet system").
• The "Semileptonic" Twist: In this specific crash, one boson behaves like a "ghost" (it decays into invisible particles or a single electron/muon), while the other boson explodes into a shower of quarks (hadrons). It's like watching a magician pull a rabbit out of a hat, but the rabbit is invisible, and the hat explodes into confetti.

2. The "Tennis Court" Analogy (Vector Boson Scattering)

The most exciting part of this discovery is how these two bosons are made. The paper focuses on a process called Vector Boson Scattering (VBS).

• The Analogy: Imagine two tennis players (quarks) hitting a ball (a boson) toward each other. Instead of just bouncing off, the balls hit each other in mid-air and scatter.
• The Signature: When this happens, the two tennis players (quarks) get knocked backward to the far corners of the stadium (the "forward" regions of the detector). They leave behind two distinct "footprints" (jets) that are far apart and have a huge amount of energy between them.
• Why it matters: This scattering is a direct test of the "rules of the game" (the Standard Model). If the Higgs boson didn't exist, these balls would bounce off with impossible energy, breaking the laws of physics. The fact that they scatter "normally" confirms our understanding of how the universe holds together.

3. The "Two Ways to Catch a Ball" (Resolved vs. Merged)

One of the challenges in this experiment is that the bosons are moving so fast that the debris they create (the "confetti") gets squashed together.

• The Resolved Method: If the boson is moving slower, the confetti spreads out enough that the detectors can see two separate small piles of debris.
• The Merged Method: If the boson is moving incredibly fast (high momentum), the two piles of confetti smash into each other and look like one giant, messy pile.
• The Innovation: The ATLAS team didn't just look for the two small piles; they developed a special technique to identify the giant, merged pile. This allowed them to see crashes that were previously invisible, effectively expanding their "searchlight" to higher energies.

4. The "AI Detective" (Machine Learning)

The data from these crashes is overwhelming. There are millions of background events (like a noisy crowd) that look very similar to the signal they want (the rare VIPs).

• To find the VIPs, the team used a Machine Learning (ML) algorithm, specifically a type of neural network called an RNN.
• Think of this AI as a super-smart bouncer at a club. It looks at the "footprints" (kinematics) and the "crowd density" (track multiplicity) of every event. It learns to distinguish between the "regular partygoers" (background noise) and the "VIPs" (the rare VBS signal) with incredible precision.

5. The Results: "We Found It!"

• The Discovery: The team analyzed data equivalent to 140 "inverse femtobarns" (a massive amount of collision data collected between 2015 and 2018).
• The Significance: They found the signal with a statistical certainty of 7.4 sigma. In the world of particle physics, 5 sigma is the gold standard for a "discovery." This result is a resounding "Yes, we see it!"
• The Measurement: They measured how often this happens (the cross-section) and found it matches the predictions of the Standard Model very closely. It's like predicting exactly how many times a specific coin flip combination will happen in a million flips, and the result matches the math perfectly.

6. The "What If?" Test (Effective Field Theory)

Finally, the scientists asked: "Could there be new, unknown physics hiding in the high-energy tail of these crashes?"

• They used a framework called Effective Field Theory (EFT) to look for "anomalous quartic gauge couplings."
• The Analogy: Imagine the Standard Model is a set of traffic laws. EFT is a way to ask, "What if there are secret, illegal shortcuts that cars are taking at super-high speeds?"
• The Outcome: They didn't find any illegal shortcuts. The data fits the standard traffic laws perfectly. However, they set the strictest limits yet on where these "illegal shortcuts" could exist. They effectively said, "If there are new physics shortcuts, they must be even more hidden than we thought."

Summary

In simple terms, the ATLAS collaboration successfully caught a rare, messy particle crash where two force-carrying particles scatter off each other. They used advanced AI to separate this signal from the noise, confirmed that the universe behaves exactly as the Standard Model predicts, and set new, tighter boundaries on where "new physics" might be hiding. It's a victory for our current understanding of the universe, while keeping the door open for future discoveries.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics relies on the mechanism of Electroweak Symmetry Breaking (EWSB), mediated by the Higgs boson. Vector Boson Scattering (VBS) is a crucial process for probing the non-Abelian gauge structure of the electroweak sector. In the absence of the Higgs boson, VBS amplitudes would violate unitarity at high energies; the Higgs mechanism ensures these amplitudes remain unitary.

• The Challenge: While VBS has been observed in fully leptonic channels (where both bosons decay to leptons), these channels suffer from low branching fractions. The semileptonic channel (one boson decaying leptonically, the other hadronically) offers a significantly higher branching fraction (factor of >2) but is plagued by large backgrounds from QCD-induced processes and top-quark production.
• The Goal: This analysis aims to observe electroweak (EWK) diboson production ($WW$, $WZ$, $ZZ$) in association with two jets ($VVjj$) in the semileptonic final state using the full Run 2 dataset. It seeks to:
  1. Measure the EWK production cross-section and signal strength.
  2. Constrain Anomalous Quartic Gauge Couplings (aQGC) using an Effective Field Theory (EFT) framework, specifically dimension-8 operators, which are sensitive to new physics at high energy scales.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collisions at $\sqrt{s}=13$ TeV collected by the ATLAS detector during 2015–2018, corresponding to an integrated luminosity of 140 fb$^{-1}$.
• Signal Generation: EWK $VVjj$processes (including VBS and non-VBS EWK contributions) were generated using **MadGraph5_aMC@NLO** at$\mathcal{O}(\alpha^6_{EWK})$.
• Backgrounds: Dominant backgrounds include $V$+jets ($W/Z$+jets), top-quark pair ($t\bar{t}$), single-top, and QCD-induced diboson production. These were simulated using Sherpa, Powheg, and Pythia.
• EFT Modeling: The Eboli model was used to introduce 21 dimension-8 operators. Signal samples included pure SM, pure BSM (anomalous), and interference terms.

Event Reconstruction and Selection

The analysis targets three decay topologies based on the number of charged leptons ($\ell = e, \mu$):

1. 0-lepton channel: $Z(\to \nu\nu) + V(\to q\bar{q})$.
2. 1-lepton channel: $W(\to \ell\nu) + V(\to q\bar{q})$.
3. 2-lepton channel: $Z(\to \ell\ell) + V(\to q\bar{q})$.

Key Reconstruction Strategies:

• Tagging Jets: Two forward jets with large rapidity separation ($\Delta\eta$) and high invariant mass ($m_{jj} > 400$ GeV) are required to identify the VBS topology.
• Hadronic Boson Reconstruction ($V_{had}$): Due to the high transverse momentum ($p_T$) of the bosons in VBS, the hadronic decay products can be collimated. The analysis employs two regimes:
  • Resolved: Two small-radius jets ($R=0.4$) reconstructing the $W/Z$ mass window (64–106 GeV).
  • Merged: One large-radius jet ($R=1.0$) with jet substructure techniques (trimming, $D_2$ variable, track multiplicity) to identify the $W/Z$ decay. This is crucial for accessing the high-$p_T$ regime ($p_T > 200$ GeV).
• Boson Tagging: A multivariate tagger based on jet mass, $D_2$, and track multiplicity is used to distinguish $W/Z$-initiated jets from QCD jets. Two working points (50% and 80% efficiency) define High-Purity (HP) and Low-Purity (LP) signal regions.

Background Estimation and Machine Learning

• Data-Driven Corrections: The modeling of $V$+jets backgrounds in the high-mass dijet region ($m_{jj}$) was found to be imperfect in simulation. A data-driven reweighting procedure was applied using Control Regions (CRs) to correct the shape of the $m_{jj}$ distribution.
• Machine Learning (ML): A Recurrent Neural Network (RNN) was developed to discriminate between the EWK signal and background.
  • Inputs: Four-momenta of jets (up to 5), track multiplicities, and for the merged regime, the four-momentum of the large-$R$ jet.
  • Architecture: LSTM layers for sequence processing (resolved) and Dense layers for large-$R$ jet information (merged).
  • Output: An RNN score used as the final discriminant in the statistical fit.

Statistical Analysis

A simultaneous binned likelihood fit was performed across all Signal Regions (SRs) and Control Regions (CRs). Nuisance parameters accounted for experimental (luminosity, jet energy scale, etc.) and theoretical uncertainties. The fit extracted the signal strength ($\mu$) and set limits on EFT Wilson coefficients.

3. Key Contributions

1. First Observation in Semileptonic Channel by ATLAS: This paper reports the first observation of EWK $VVjj$ production in the semileptonic channel by the ATLAS Collaboration, utilizing the full Run 2 dataset.
2. Merged Regime Sensitivity: It demonstrates the critical role of the merged jet regime (large-$R$ jets) in enhancing sensitivity to high-$p_T$ VBS events and EFT effects, which are inaccessible with resolved jets alone.
3. Advanced ML Application: The successful deployment of an RNN architecture to handle variable jet multiplicities and complex kinematic correlations in a semileptonic VBS analysis.
4. Comprehensive EFT Limits: It provides the first set of exclusion limits on dimension-8 EFT operators (aQGC) in the semileptonic channel by ATLAS, covering 19 operators.

4. Results

• Observation: The EWK $VVjj$ production is observed with a significance of 7.4$\sigma$ (expected 6.1$\sigma$), exceeding the 5$\sigma$ threshold for discovery.
• Signal Strength: The measured signal strength relative to the SM prediction is:
  $$\mu_{EWK} = 1.28^{+0.23}_{-0.21}$$
  This is consistent with the SM prediction within 1.5$\sigma$.
• Fiducial Cross Section: The measured fiducial cross section is $\sigma_{fid} = 29.2 \pm 4.9$ fb (SM expectation: $20.4 \pm 3.5$ fb).
• EFT Constraints: No significant deviation from the SM was observed. The analysis set 95% confidence level (CL) limits on Wilson coefficients ($f/\Lambda^4$) for various dimension-8 operators.
  • Example Limits:
    • $f_{S02}/\Lambda^4$: $(-3.96, 3.96)$ TeV$^{-4}$
    • $f_{T0}/\Lambda^4$: $(-0.25, 0.22)$ TeV$^{-4}$
    • $f_{M0}/\Lambda^4$: $(-1.26, 1.25)$ TeV$^{-4}$
  • These limits improve upon previous ATLAS results in other channels for scalar ($f_S$) and mixed ($f_M$) operators, with improvements up to a factor of 3.3 for certain operators.

5. Significance

This work represents a major milestone in the study of electroweak symmetry breaking and the search for new physics at the LHC.

• Validation of SM: The observation confirms the SM prediction for EWK diboson production in a challenging, high-background environment, validating the gauge structure of the theory.
• New Physics Reach: By probing high invariant mass and high-$p_T$ regimes via the semileptonic channel and merged jets, the analysis extends the sensitivity to anomalous quartic gauge couplings beyond previous limits.
• Methodological Benchmark: The combination of large-radius jet substructure, data-driven background corrections, and deep learning (RNN) sets a new standard for future analyses of complex multi-jet final states at the LHC and the High-Luminosity LHC (HL-LHC).
• Complementarity: The results complement fully leptonic and hadronic searches, providing a more complete picture of the electroweak sector and constraining BSM models that predict enhanced VBS at high energies.